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Numerical study of a high-order quasiconserved quantity in the Hénon-Heiles problem
Phys. Rev. E 48, 2288 – Published 1 September, 1993
DOI: https://doi.org/10.1103/PhysRevE.48.2288
Abstract
Recent efforts to derive and study a quasiconserved quantity K in the Hénon-Heiles problem in terms of a single set of variables are discussed. Numerical results are given, showing how the value of such a quantity varies with time and order in a power-series expansion for K in terms of monomials of the coordinates and velocities. The lowest order in the power series for K corresponds to n=4 and the highest order to n=27, so that 24 orders are included in the series. The results are compared with an earlier study by the authors [Phys. Rev. A 42, 1931 (1990)] that included an expansion for K for orders n=4 to n=15. In general, even in regions where the earlier study suggested that the series for K might be converging, our more recent results [Phys. Rev. A 44, 925 (1991)], involving twice as many orders, suggest that the series diverges.
References (6)
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- In FJS1 we used MACSYMA_ from Symbolics, Inc. In FJS2 and this paper we have used MAPLE_ from Waterloo Maple Software, Inc.